We define p# (p-primorial) to be the
product of the primes less than or equal to p. For
example:

3# = 2.3 = 6,

5# = 2.3.5 = 30, and

13# = 2.3.5.7.11.13
= 30030.

This is also called p-prime factorial.
Euclid's proof that there are infinitely many primes
provides what may be the first use of p# (the
concept, not the notation).

It is customary to only apply the notation p# to
primes p, but some authors will apply it to any
positive real number (e.g., 10.72# =
2.3.5.7 = 210).
When viewed this way, the function log(x#) is
Tschebycheff's function, and the prime number theorem is equivalent to the expression